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VOL. 8 | 1984 Morse inequalities and estimates for the number of solutions of nonlinear equations
E.N. Dancer

Editor(s) Neil S. Trudinger, Graham H. Williams

Abstract

In this lecture, I want to discuss how Morse inequalities apply in more general situations where mappings are not bounded below, where there are degenerate critical points, and where we have some informa·tion of hmv solutions of the corresponding differential equations join critical· points. We then discuss an application to elliptic partial differential equation and some counterexamples which show that our estimates for the number of solutions of the elliptic problem are, in a sense, best possible. The proof of most of the results given depend upon the homotopy index of Conley [3]. However, nearly all the results can be understood without: knowing the homotopy index.

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Published: 1 January 1984
First available in Project Euclid: 18 November 2014

zbMATH: 0568.58034
MathSciNet: MR799207

Rights: Copyright © 1984, Centre for Mathematical Analysis, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.

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Vol. 8 • 1 January 1984
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